A novel image encryption scheme based on DCT transform and DNA sequence

Indonesian Journal of Electrical Engineering and Computer Science
Vol. 21, No. 3, March 2021, pp. 1455~1464
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v21.i3.pp1455-1464  1455
Journal homepage: http://ijeecs.iaescore.com
A novel image encryption scheme based on DCT transform and
DNA sequence
Ali A.Yassin1
, Abdullah Mohammed Rashid2
, Abdulla J. Yassin3
, Hamid Alasadi4
1,3,4
Computer Science Department, Education College for Pure Science, University of Basrah, Basrah, Iraq
2
Education College for Human Science, University of Basrah, Basrah, Iraq
Article Info ABSTRACT
Article history:
Received Oct 10, 2020
Revised Dec 7, 2020
Accepted Dec 23, 2020
Recently, the concept of DNA has been invested in computing technology in
different ways which linking information technology and biological sciences.
However, the DNA encryption scheme has drawbacks such as expensive
experimental equipment and hard to hold its biotechnology. Additionally,
during careful cryptanalysis that applied to most of these image encryption
schemes, we notice that DNA can only influence one DNA base, which
causes poor diffusion. Our proposed scheme is not applied complex
biological operation but just is given to improve the diffusion ability of
image encryption scheme by using DNA sequence and DCT transform.
Furthermore, empirical results on real images and security analysis
demonstrate that our scheme not only has flexibility and efficiency
encryption scheme but also has the ability to resist well-known attacks such
as entropy attack and statistical attack. Additionally, our work enjoys several
strong characteristics as follows: (1) the decryption error is very low to
recover the original image; (2) Once key for each encryption process and if
the user wants to use the same key in many times, our scheme supports secret
key sensitivity; (3) the value of correlation of the encrypted image is null.
Keywords:
Cryptanalysis
DCT transform
DNA sequence
Image encryption
This is an open access article under the CC BY-SA license.
Corresponding Author:
Abdulla J. Yassin
Computer Science Department
Education College for Pure Science
University of Basrah. Iraq 42001
Email: abdullajas@uobasrah.edu.iq
1. INTRODUCTION
In the last years, the communication and network systems have been changed due the information
technology and Internet. At the present time, ten-thousands of kilobytes of trusted information are transferred
in Internet over insecure communication channels, the information may be exposed to interrupting by an
adversary that tries to obtain or change information. The protected communication method is that an user
(sender) encrypts the original image in to encrypted image based on certain encryption method and only the
legal receiver has ability to decrypt the encrypted image with the secret key(s) to retrieve the sender's image.
There are many mainly schemes for image encryption such as diffusion (by using pixel replacement),
permutation (by using pixel scrambling), or both diffusion and permutation. Furthermore, we find several
applications of image encryption in many fields such as video conference, military, biometric systems,
personal image. These applications require strong encryption scheme that has a good balanced between
security and performance. There are several studies appear recently used DNA in cryptography [1-3].
Conversely, several image encryption schemes have been presented for both gray image and real
image, for instance, partial encryption, DNA cryptography, transform domain, and modern cipher text but

 ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 21, No. 3, March 2021 : 1455 - 1464
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most of these schemes have vulnerabilities [4]. Continuously, the modern cryptography methods such as
advanced encryption standard (AES), data encryption standard (DES), international data encryption
algorithm (IDEA), etc., are strong algorithms for plain text encryption, but they have many drawbacks when
applied in image encryption [5, 6], because they cannot resist the attaches. Shah & Farooq [7], using an
algorithm called SERPENT chain ring-based to encrypt the image by utilizing the set of boxes each one 128
bites, which meet the high level of performance but low efficiency. From other Chen et al, [8] Chen et al,
proposed an encryption approach that classified an excellent due the features of chaos such as periodicity.
Our proposed scheme is forceful against chosen/known plain image attack and can use one
permutation-diffusion round for encryption function. Moreover, a security analysis is critical to prove the
strength and efficiency of the encryption function against the most common attacks. Additionally, the presented
encryption scheme has several advantages such as high encryption rate, involves less computation, and suitable
to small modifications in the secret key of image encryption. Continuously, the key is generation once time for
each encryption function so even with the knowledge of the estimated key values, the adversary does not has
possibility to attack the cipher text. Finally, Table 1 explains the main differences among our proposed scheme
and related works. The rest of paper is classified as follows. Section 2 views primitive tools used in the present
schemewhile Section 3 focuses on the proposed scheme. The experimental results are viewed in the Section 4.
The security analysis presents in the Section 5. Finally, the Section 6 indicates of the conclusion.
Table 1. Comparison of image encryption schemes
Scheme C1 C2 C3 C4 C5 C6 C7 C8 C9
Patidar et al. [9] Md No Md No No No Variable Md Md
Wang et al. [10] Md No Variable No No Yes Variable Md Md
Li et al .'s al. [11] Md No Variable No No Yes Variable Md Md
Tong et al. [12] Variable No Md No No No Md Md Md
Zhang et al.(2009) [13] Md No High Yes Yes No Variable Md Md
Xue et al. [14] Md No High Yes Yes Yes High High Md
Murillo-Escobar et al. (2014) [15] Md No Variable Yes Yes Yes High High Md
Zhou et al. (2014) [16] Variable No High No No No Variable Md Md
Our Proposed scheme Md Yes High Yes Yes Yes High High High
C1:Key Space; C2:One Time Key; C3:Time Encryption; C4: Entropy; C5:DNA; C6: Chosen plain image attack; C7: Imperceptibility;
C8: Visual Degradation; C9: Cryptographic Security.
2. PRIMITIVE TOOLS
2.1. DNA and digital image
A DNA sequence composed of the main four nucleic acid cores as follows. A (adenine), C
(cytosine), G (guanine), T (thymine), where A and T are corresponding, G and C are corresponding [17].
Based on four cores A, C, G and T for applying encoded function on 00, 01, 10 and 11, there are 24 types of
coding manners. But there are only 8 type of coding manners fulfill the Watson-Crick complement law,
which are viewed in Table 2. Our proposed scheme focuses to use the DNA code for encoding the input
images. For the 24 bits color image, we divide into three layers (Red, Green, Blue), for the 8 bits for each
layer, each layer's pixel can be related with the DNA sequence whose length connects with 4 (normally, the
length of binary sequence is 8).
Table 2. Eight types of methods encoding and decoding map rule of DNA sequence
1 2 3 4 5 6 7 8
00 00 01 01 10 10 11 11
11 11 10 10 01 01 00 00
01 10 00 11 00 11 01 10
10 01 11 00 11 00 10 01
2.2. The algebraic operations in DNA sequences
With the fast progresses of DNA development technology, the authors [18-19] presented mixed
operation based on some biology operations, algebraic operations, and DNA sequence. Furthermore, addition
and subtraction operations for DNA sequences are implemented according to conventional addition and
subtraction in the binary system. Corresponding to 8 types of DNA encoding methods, there also exist 8
types of DNA addition rules and 8 types of DNA subtraction rules that are viewed in Tables 2 and 3,
respectively. From Tables 2, 3 and 4, we notice that any one rule base in each row or column is single,
consequently, the result of addition and subtraction operations consider uniquely result.

Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 
A novel image encryption scheme based on DCT transform and DNA sequence (Ali A.Yassin)
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Table 1. One type of addition operation for DNA sequences
Table 2. One type of subtraction operation for DNA sequences
-
T
A T
2.3. XOR operation for DNA sequences
In practice, XOR operation for DNA sequences is implemented accommodating to conventional
XOR in the binary. There are eight types of DNA encoding methods that lead to exist eight types of DNA
XOR rules. In our proposed scheme, the XOR operation plays main role to fusion the input image and the
key image. For instance, assume we have two DNA sequences such as [GATC] and [TGCT], we use one
type of XOR operation which is viewed in Table 5 to XOR them and we can obtain the sequence [CGGG] as
a result. In this paper, the main aim of using XOR operation is to scramble the pixel values of
the input image [20].
Table 5. XOR operation with DNA sequences
C
C
G
2.4. DCT transform
Generally, the discrete cosine transform considers one of the most widespread transforms that has
been used in many fields such as image compression. It has several advantages like clearly of computation
where inverse of DCT can be easily computed. To get high correlation of image data, the DCT supports an
effectual compaction and has the property of reparability [21]. Based on (1) in two-dimensional state, the
DCT runs on N by N block of image's pixels like X, and its result represents by blocks with N by N block of
image's pixels like Y.
𝑌𝑥𝑦 =
2
𝑁
𝐶𝑥𝐶𝑦 ∑ ∑ 𝑥𝑖,𝑗 cos (2𝑖+1)𝑥𝜋
2𝑁
𝑁−1
𝑗=0
𝑁−1
𝑖=0 cos(2𝑗+1)𝑥𝜋
2𝑁
𝐶𝜕 = {√1
2
𝜕 = 0
1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(1)
where Y is an element in set of N by N coefficients demonstrating of the data in the transformed domain. The
set of data in waveforms is referred for each probable value of N (typically N=8, thus there is 64 waveforms).
3. OUR PROPOSED SCHEME
In this section, we propose a new image encryption scheme based on DNA encoding sequence and
DCT transformation. The following notations in Table 6 will be used throughout our scheme. The proposed
encryption scheme includes three components: original image, key image, and encryption image. Figure 1
explains the essential differences between the proposed scheme and the traditional image encryption scheme.
Our work consists of four phases-setup of secret key, DCT, encryption process, and decryption process.

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(a) Block diagram of the traditional image encryption
(b) Basic architecture of our proposed image encryption scheme
Figure 1. The proposed scheme feature (a) traditional method, (b) proposed method
Table 6. Notations of symbols used in proposed scheme
Symbol Description
𝐷𝐶𝑇 Discrete Cosine transformation.
𝑖𝑑𝑐𝑡 inverse discrete cosine transformation.
𝑁 The number of rows in original image 𝑖𝑚𝐼 .
𝑀 The number of columns in original image 𝑖𝑚𝐼 .
𝑖𝑚ℎ hash matrix.
ℎ crypto-hash function (SHA-512).
𝑖𝑚𝑘 image key.
𝑖𝑚𝐴𝑠𝑐𝑖𝑖 Ascii Code matrix that is used to get binary code for each symbol and then the result of this step is 𝑖𝑚𝐵 .
𝑖𝑚𝐵 Binary matrix for each element in 𝑖𝑚𝐴𝑠𝑐𝑖𝑖 .
𝑖𝑚𝑟 Random matrix is used for getting image key 𝑖𝑚𝑘 based on DNA sequence.
𝑖𝑚𝐼 Input color image.
𝐷𝐶𝑇 Discrete cosine function
𝑖𝑑𝑐𝑡 Inverse Discrete cosine function
𝐷𝐶𝑅,𝐷𝐶𝐺 , 𝐷𝐶𝐵
The DC coefficients of color image; where, R is read layer of image, G is green layer of image, and B is blue
layer of image.
𝐷𝐶𝑅
′
, 𝐷𝐶𝐺
′
, 𝐷𝐶𝐵
′
The DC coefficients of color image after applied DNA sequence.
𝐴𝐶𝑅 , 𝐴𝐶𝐺 , 𝐴𝐶𝐵 The AC coefficients of color image.
𝑆 Integer random number that is used to encrypt AC coefficients to obtain (𝐴𝐶𝑅
′
, 𝐴𝐶𝐺
′
, 𝐴𝐶𝐵
′
).
𝐴𝑐𝑐𝑢𝑚 Accumulate function to get color image from main layer (Red, Green, Blue).
Md Moderate
3.1. Setup of secret key
This phase focuses on key image that is generated by using a random image 𝑖𝑚𝑟 based on the
randomly generator. Then use the random function to create N×M integer matrix. So, the N and M
represented the size of original image (𝑖𝑚𝐼 ) which submits to our proposed scheme for encrypted it. This

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case of image's key considers more appropriate compared with the average of template image. To build
secure key, our proposed schemes performs the following steps:
a) Apply crypto-hash function (SHA-512) on each 512 pixel of image key(𝑖𝑚𝑘 ) ∈ 𝑍N×M
∗
. The output of
this step is hash matrix 𝑖𝑚ℎ = ℎ(𝑖𝑚(0..512), 𝑖𝑚(512..1024) … ., 𝑖𝑚(𝑁0..N×M) ) that consists of alphabetic and
numeric symbols (alphabetical and numerical).
b) Convert hash matrix into Ascii Code matrix 𝑖𝑚𝐴𝑠𝑐𝑖𝑖 based on table of Ascii Code. After that, each
elements of 𝑖𝑚𝐴𝑠𝑐𝑖𝑖 convert in binary sequence to generate a new matrix 𝑖𝑚𝐵 .
c) Use the eight kinds of DNA encoding schemes in Table 2 to obtain key image 𝑖𝑚𝑟 that depends on
convert each twice binary bits from binary mode to DNA mode selecting one rule for each encryption
phase. So, when user wishes to encrypt the same or other image again, he should be generated a new
image key and uses another DNA's rule. This process prevents many attacks such as plain image attack,
MITM attack, and generate once key for each encryption process. Finally, we obtain the secret image key
based on DNA sequence (𝑖𝑚𝑘 ).
3.2. DCT transform
The main steps of the DCT are explained as follows (as demonstrated in Figure 2):
a) Input the color original image (𝑖𝑚𝐼 ) and divided it into three layers (Red (𝑖𝑚𝑅 ), Green (𝑖𝑚𝐺 ),
Blue (𝑖𝑚𝐵 )).
b) Apply DCT to gain coefficient matrices on each layers (𝑖𝑚𝑅 , 𝑖𝑚𝐺 , 𝑖𝑚𝐵 ). In coding by using DCT
transform, each layer of original image 𝑖𝑚𝐼 ) is separated into 8*8 blocks and DCT transform is applied
on each block. After that, these coefficients should be quantized based on JPEG compression standard
matrix. Each pixel value of input image is split by the matching value of quantization matrix. We notice
the first coefficient knowingly DC coefficient has the most energy and the other coefficients knowingly
AC have the important details of input image. The DCT splits the image into several frequencies that is
low frequencies locates on left top corner of original image. In the encryption process, the AC coefficients
can be only reduced quality of the original image in the encrypted state and is actionable for reducing
image resolution in marketable applications. Additionally, the coefficient with low frequency (non-zero)
in both dimensions is related with DC coefficient and the remaining 66 coefficients are connected with
the AC coefficients with high frequencies. This way recuperates the original images by statistical models
and the cipher text-only attack [22]. Furthermore, taking in account the point stream encryption function
is used, image key sequence with the original image is sound Xor, as a result any coefficient has ability to
encrypt by a specific number of bits from key sequence. Figure 3 explains the drawbacks of AC
coefficients as well as we focus on using DC and AC in clever manner. The output of this phase is
(ACR , ACG , ACB , DCR , DCG , DCB ) represent useful parameters in the next phases.
Figure 2. The main steps to generate key image
[23]

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(a) (b) (c) (d)
Figure 3. Encrypted and recovered image based on AC coefficients (a) Gray image, (b) Encrypted image, and
(c) Decrypted image (d) Restored image
3.3. Encryption process
In this phase, the proposed encryption scheme includes three steps as follows:
a) The DC coefficients are encoded into DNA sequences matrices (𝐷𝐶𝑅 , 𝐷𝐶𝐺 , 𝐷𝐶𝐵 ). The result of this step
is (𝐷𝐶𝑅
′
, 𝐷𝐶𝐺
′
, 𝐷𝐶𝐵
′
).
b) The AC coefficients of original image is permutated under the scramble method. In this phase, image
scrambling applied on AC matrices (𝐴𝐶𝑅 , 𝐴𝐶𝐺 , 𝐴𝐶𝐵 ) proceeds coding to the pixel values of the AC
matrices changing the values of the matrices' elements. So, we notice the histograms of the scrambling
matrices (𝐴𝐶𝑅
′
, 𝐴𝐶𝐺
′
, 𝐴𝐶𝐵
′
) and the original matrices (𝐴𝐶𝑅 , 𝐴𝐶𝐺 , 𝐴𝐶𝐵 ) are then different. An introduction
of AC matrix scrambling method based on element value switching using X-OR operation is given below:
- Assuming that the size of the matrix is N×M, a random integer numbers sequence 𝑆 = {𝑆1, 𝑆2,
𝑆3, … , 𝑆N×M} is created to use with AC matrices in the next step.
- The scrambling operation is applied on each layer of AC matrices (𝐴𝐶𝑅 , 𝐴𝐶𝐺 , 𝐴𝐶𝐵 ) with sequence 𝑆
as follows:
c) In this step, using XOR operation to encrypt each image key (𝑖𝑚𝑘 ) with DNA coding (𝐷𝐶𝑅
′
, 𝐷𝐶𝐺
′
,
𝐷𝐶𝐵
′
) and scrambling matrices (𝐴𝐶𝑅
′
, 𝐴𝐶𝐺
′
, 𝐴𝐶𝐵
′
).
- Apply inverse discrete cosine transform to restore image into spatial domain for each layers 𝑖𝑚𝑅
′
=
𝑖𝑑𝑐𝑡(𝐴𝐶𝑅
′
, 𝐷𝐶𝑅
′
), 𝑖𝑚𝐺
′
= 𝑖𝑑𝑐𝑡(𝐴𝐶𝐺
′
, 𝐷𝐶𝐺
′ ), 𝑖𝑚𝐵
′
= 𝑖𝑑𝑐𝑡(𝐴𝐶𝐵
′
, 𝐷𝐶𝐵
′
).
- 𝑖𝑚𝑅𝐸 =𝑖𝑚𝑅
′ ⨁ 𝑖𝑚𝑘 , 𝑖𝑚𝐺𝐸 =𝑖𝑚𝐺
′
⨁ 𝑖𝑚𝑘 , 𝑖𝑚𝐵𝐸 = 𝑖𝑚𝐵
′ ⨁ 𝑖𝑚𝑘 .
- Then, the output of this step is (𝑖𝑚𝐸 = 𝐴𝑐𝑐𝑢𝑚(𝑖𝑚𝑅𝐸 , 𝑖𝑚𝐺𝐸 , 𝑖𝑚𝐵𝐸 )) where 𝐴𝑐𝑐𝑢𝑚 is function that
used to accumulate all layers of image encryption.
3.4. Decryption process
The main steps of this phase as follows.
a) Split encryption image (𝑖𝑚𝐸 ) into three layers based on major color red, green, and blue. 𝑖𝑚𝐸
𝑆𝑝𝑙𝑖𝑡
→ 𝑖𝑚𝑅𝐸 , 𝑖𝑚𝐺𝐸 , 𝑖𝑚𝐵𝐸 .
b) Apply shared key 𝑖𝑚𝑘 to retrieve (𝑖𝑚𝑅
′
, 𝑖𝑚𝐺
′
, 𝑖𝑚𝐵
′
) where each layer decrypts as follows. 𝑖𝑚𝑅
′
=
𝑖𝑚𝑅𝐸 ⨁ 𝑖𝑚𝑘 , 𝑖𝑚𝐺
′
= 𝑖𝑚𝐺𝐸 ⨁ 𝑖𝑚𝑘 , 𝑖𝑚𝐵
′
= 𝑖𝑚𝐵𝐸 ⨁ 𝑖𝑚𝑘 .
c) Using discrete cosine transform (DCT) for each layer to retrieve the useful factors (𝑖𝑚𝑅𝐸
𝐷𝐶𝑇
→ 𝐴𝐶𝑅
′
, 𝐷𝐶𝑅
′
,
𝑖𝑚𝐺𝐸
𝐷𝐶𝑇
→ 𝐴𝐶𝐺
′
, 𝐷𝐶𝐺
′
, 𝑖𝑚𝐵𝐸
𝐷𝐶𝑇
→ 𝐴𝐶𝐵
′
, 𝐷𝐶𝐵
′
).
d) Recover DC coefficients (𝐷𝐶𝑅 , 𝐷𝐶𝐺 , 𝐷𝐶𝐵 ) based on DNA rule in Table 2.
e) Retrieve AC coefficients (𝐴𝐶𝑅 , 𝐴𝐶𝐺 , 𝐴𝐶𝐵 ) by using sequence 𝑆 = {𝑆1, 𝑆2, 𝑆3, … , 𝑆n×m}. Where 𝐴𝐶𝑅 =
𝑆 ⨁ 𝐴𝐶𝑅
′
, 𝐴𝐶𝐺 = 𝑆 ⨁ 𝐴𝐶𝐺
′
, 𝐴𝐶𝐵 = 𝑆 ⨁ 𝐴𝐶𝐵
′
.
f) Apply inverse discreet cosine transform to return the image from sequential domain to spatial domain.
𝑖𝑚𝑅 = 𝑖𝑑𝑐𝑡(𝐴𝐶𝑅 , 𝐷𝐶𝑅 ), 𝑖𝑚𝐺 = 𝑖𝑑𝑐𝑡(𝐴𝐶𝐺 , 𝐷𝐶𝐺 ), 𝑖𝑚𝐵 = 𝑖𝑑𝑐𝑡(𝐴𝐶𝐵 , 𝐷𝐶𝐵 ). Then, use
𝐴𝑐𝑐𝑢𝑚 function to obtain color image where𝑖𝑚𝐼
′
= 𝐴𝑐𝑐𝑢𝑚(𝑖𝑚𝑅 , 𝑖𝑚𝐺 , 𝑖𝑚𝐵 )
In this section, we address the scenario of our proposed scheme between two parties (Alice and
Bob) in a privacy-preserving method without losing any useful information of encryption image. Figure 4
demonstrates image encryption and decryption of our proposed scheme.
Alice Side (𝑨𝒍𝒊𝒄𝒆 → 𝑩𝒐𝒃: imE ):

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Given image imI , Alice would like to encrypt imI and then applies our proposed scheme to obtain encrypted
image imE . Then, he submits imE to Bob.
Bob Side (𝑩𝒐𝒃 → 𝑩𝒐𝒃: 𝑖𝑚𝐼 ):
Upon receiving the encrypted image in encryption process from Alice, Bob decrypts imE based on
decryption process in our proposed scheme to get color image based on important information
(𝑖𝑚𝐾 , 𝑆, 𝐷𝑁𝐴 𝑟𝑢𝑙𝑒) which both parties (Bob and Alice) are agreement it in setup phase.
3.5. Security analysis and experimental evaluation of our proposed scheme
We focus on security analysis and experimental results in this section.
Proposition 1. Our proposed scheme has ability to prevent of forgery and parallel-session attacks.
Proof. If an attacker attempts to impersonate the Alice/Bob, access to a valid session image encryption (𝑖𝑚𝐸 )
through secret parameters (𝐷𝑁𝐴 𝑟𝑢𝑙𝑒𝑠, 𝑖𝑚𝑟 , 𝑖𝑚ℎ , 𝑖𝑚𝐴𝑠𝑐𝑖𝑖 ) will be required. Since the attacker will not
possess any knowledge of ( 𝑖𝑚𝑘, 𝑆) required to calculate 𝐷𝐶𝑅
′
, 𝐷𝐶𝐺
′
, 𝐷𝐶𝐵
′
, 𝐴𝐶𝑅
′
, 𝐴𝐶𝐺
′
, 𝐴𝐶𝐵
′
and then apply
encryption function as follows:
1. 𝑖𝑚𝑅𝐸 =𝑖𝑚𝑅
′ ⨁ 𝑖𝑚𝑘 , 𝑖𝑚𝐺𝐸 =𝑖𝑚𝐺
′
′ ⨁ 𝑖𝑚𝑘
2. 𝑖𝑚𝐸 = 𝐴𝑐𝑐𝑢𝑚(𝑖𝑚𝑅𝐸 , 𝑖𝑚𝐺𝐸 , 𝑖𝑚𝐵𝐸 )
So, this type of attacks will be averted and an attacker cannot apply these type of attacks.
Figure 4. Encryption and decryption of our proposed scheme
Proposition 2. Our proposed scheme can withstand Chosen/known plain image attack.
Proof. There are several significant points that connected with our proposed scheme to avoid this malicious
attack as below:
1. The permutation diffusion process is realized in one phase according to scrambling method that has been
applied in our proposed scheme, we use the scrambling method in partial manner as follows.
a. 𝑖𝑚𝑅
𝐷𝐶𝑇
→ 𝐴𝐶𝑅 , 𝐷𝐶𝑅 ; 𝑖𝑚𝐺
𝐷𝐶𝑇
→ 𝐴𝐶𝐺 , 𝐷𝐶𝐺 ; 𝑖𝑚𝐵
𝐷𝐶𝑇
→ 𝐴𝐶𝐵 , 𝐷𝐶𝐵 .
b. The scrambling is applied on each layer of AC matrices (𝐴𝐶𝑅 , 𝐴𝐶𝐺 , 𝐴𝐶𝐵 ) with sequence 𝑆 :
𝐴𝐶𝑅
′
= 𝑆 ⨁ 𝐴𝐶𝑅 , 𝐴𝐶𝐺
′
= 𝑆 ⨁ 𝐴𝐶𝐺 , 𝐴𝐶𝐵
′
= 𝑆 ⨁ 𝐴𝐶𝐵 .
2. The DNA encryption sequence is applied on DC coefficients (𝐷𝐶𝑅 , 𝐷𝐶𝐺 , 𝐷𝐶𝐵 ) of input image (𝑖𝑚𝐼 ) for
obtaining DNA sequences matrices (𝐷𝐶𝑅
′
, 𝐷𝐶𝐺
′
, 𝐷𝐶𝐵
′
) based on the secret key (𝑖𝑚𝑘) and DNA rules in
Table 7. Additionally, we use crpto-hash function for each 512 pixels of 𝑖𝑚𝑟 that gains our proposed
scheme strong secure against this attack.
3. The encrypted image is transformed and rounded to 𝑖𝑚𝑘 ∈ [0. .255] for each layer (𝑖𝑚𝑅𝐸 =𝑖𝑚𝑅
′ ⨁ 𝑖𝑚𝑘 ,
𝑖𝑚𝐺𝐸 =𝑖𝑚𝐺
′
′ ⨁ 𝑖𝑚𝑘 ) in the encryption process (𝑖𝑚𝐸 = 𝐴𝑐𝑐𝑢𝑚(𝑖𝑚𝑅𝐸 , 𝑖𝑚𝐺𝐸 , 𝑚𝐵𝐸 ).

 ISSN: 2502-4752
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Table 7. One time key in encryption process
Key Layer Correlation
Key 1 Vs. Key2
0.0034
0.00087
0.00267
Key 2 Vs. Key3
0.0022
0.00076
0.00156
In a chosen plain image attack, the cryptanalyst refers that there is temporal access at encryption
equipment and he can select a color image for encryption and attempt to find the image secret key (𝑖𝑚𝑘 )
based on the following important points:
1. He selects a random image and split into three layers 𝑖𝑚𝐼
𝑆𝑝𝑙𝑖𝑡
→ 𝑖𝑚𝑅 , 𝑖𝑚𝐺 , 𝑖𝑚𝐵 .
2. He tries to build 𝑖𝑚𝑘 or eavesdrops it from the last session of encrypted image between Bob and Alice.
3. He compute 𝑖𝑚𝑅
𝐷𝐶𝑇
→ 𝐴𝐶𝑅 , 𝐷𝐶𝑅 ; 𝑖𝑚𝐺
𝐷𝐶𝑇
→ 𝐴𝐶𝐺 , 𝐷𝐶𝐺 ; 𝑖𝑚𝐵
𝐷𝐶𝑇
→ 𝐴𝐶𝐵 , 𝐷𝐶𝐵 .
4. The cryptanalyst is facing severe difficulties to encrypt DC and AC coefficients because he should know
the DNA sequence rule and scrambling sequence, respectively to generate (𝐷𝐶𝑅
′
, 𝐷𝐶𝐺
′
, 𝐷𝐶𝐵
′
, 𝐴𝐶𝑅
′
, 𝐴𝐶𝐺
′
,
𝐴𝐶𝐺
′
). While the key has generated in the previous session worked once for each encryption phase.
Therefore, we have different DNA and scrambling sequences for each plain image (𝑖𝑚𝐼 ).
Proposition 3. Our proposed scheme can withstand entropy image attack.
Proof. The entropy controls the changeability of message/plaintext, i.e. it measures how much unrest
generates the encryption function at output. If the scrambling process works well, we have high trouble in
encrypted image, as a result, higher refers to entropy. Another situation, the encryption function is not
adequately random and the cryptosystem may be applied the fruitful entropy attack because there occurs a
certain degree of changeability of the encryption process. Herein, the performance of our proposed
encryption process is tested and verified. Additionally, the entropy H(𝑝) of plaintext (𝑝) can be computed as
follows:
𝐻(𝑝) = ∑ 𝑃𝑟𝑜𝑏(𝑝𝑖)𝑙𝑜𝑔2(1/𝑃𝑟𝑜𝑏(𝑝𝑖))
2𝑁−1
𝑖=1
where N is the number of bits of the plaintext 𝑝, 2𝑁
refers to all possible values, 𝑃𝑟𝑜𝑏(𝑝𝑖) denotes a
probability of 𝑝𝑖, 𝑙𝑜𝑔2 characterize the base 2 logarithm, and an entropy represents expressed in bits, If there
is the plaintext 𝑝 encrypted with 2𝑁
possible values, the entropy must be 𝐻(𝑝) = 𝑁 perfectly. The true image
has 8 bits per layer (Red, Green, Blue), i.e.𝑁 = 8 at element layer. Consequently, the maximum entropy of
each element in true image is 8. Table 8 demonstrates the results of entropy and a comparison with modern
related works. The value of entropy is close to 8, so, the scrambling and DNA sequences process are good
and obtaining high unrest at output.
Table 8. Correlation coefficient of encrypted image
Color
Image
Layer
Our Proposed
Scheme
Murillo-Escobar et al.[24]
(2015)
Zhou et al. [16]
(2014)
Zhang et al. [25]
(2013)
256×256
R 7.9922 7.9949
7.9976
G 7.9911 7.9953
B 7.9909 7.9942
512×512
R 7.9933 7.9974
7.9993 7.9993
G 7.9922 7.9975
B 7.9911 7.9969
1024×1024
R 7.9922 7.9978
7.9998
G 7.9923 7.9976
B 7.9943 7.9976
3.5. Computation cost
We computed the costs of the different process (Setup of secret key, DCT transform, encryption
process and decryption process) in the proposed scheme based on Table 9. Table 10 explains the time
processing of our proposed scheme.

1463
Table 9. Description of time processing
Notation Description
Th Time of Process hash function
TDNA Time of DNA Process
T dct Time of discrete cosine transform (𝑑𝑐𝑡)
T idct Time of inverse discrete cosine transform (𝑖𝑑𝑐𝑡)
TEnc / Dec Encryption and Decryption process
Table 10. Computational cost
Process Time
Setup of Secret Key Th + TDNA
DCT transform 3 TDNA
Encryption Process 3 TDNA + 3 T dct + 3 TEnc + 3 T idct
Decryption Process 3 TDNA + 3 T dct + 3 T Dec+ 3 T idct
Total Th + 10 TDNA + 6 T dct + 6 T idct + 6 TEnc / Dec
4. CONCLUSION
In this paper, we have proposed a robust and an efficient encryption scheme for color image. We
used DCT, DNA, ands scrambling method to achieve a good balance between strong security and time
processing of proposed scheme. The security analysis approves that the color image encryption has a good
performance and safe against many well-known attacks such as MITM attack, entropy attack image attack,
differential attack, static attack, chosen/known plain image attack. Additionally, our work enjoys several
strong characteristics as follows: (1) the decryption error is very low to recover the original image; (2) Once
key for each encryption process and if the user wants to use the same key in many times, our proposed
scheme supports secret key sensitivity; (3) the encrypted image is null based correlation value.
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